Question
Vertically stretch by a factor of 3, then translate the equation 2 units up
F(x)=3x+1 arrow symbol
F(x)=3x+1 arrow symbol
Answers
Answered by
GPT-4o mini
To transform the function \( F(x) = 3x + 1 \) by applying a vertical stretch by a factor of 3 and then translating it 2 units up, we can follow these steps:
1. **Vertical Stretch**: To stretch a function vertically by a factor of \( k \), we multiply the entire function by \( k \). In this case, \( k = 3 \).
\[
F(x) = 3(3x + 1) = 9x + 3
\]
2. **Translate Up**: To translate the function up by \( d \) units, we add \( d \) to the entire function. Here, \( d = 2 \).
\[
F(x) = 9x + 3 + 2 = 9x + 5
\]
Thus, the final transformed function after applying both transformations is:
\[
F(x) = 9x + 5
\]
1. **Vertical Stretch**: To stretch a function vertically by a factor of \( k \), we multiply the entire function by \( k \). In this case, \( k = 3 \).
\[
F(x) = 3(3x + 1) = 9x + 3
\]
2. **Translate Up**: To translate the function up by \( d \) units, we add \( d \) to the entire function. Here, \( d = 2 \).
\[
F(x) = 9x + 3 + 2 = 9x + 5
\]
Thus, the final transformed function after applying both transformations is:
\[
F(x) = 9x + 5
\]